Space enclosing structure

ABSTRACT

A space enclosing structure formed from a plurality of trapezoidal structural elements. The trapezoidal elements are assembled in groups of five each to form a plurality of pentagonal based, truncated pyramidal modules. The modules in turn are assembled in abutting base edge-to-base edge relationship to form at least a portion of a spheroid.

[451 Dec. 17, 1974 SPACE ENCLOSING STRUCTURE [76] Inventor: Robert Lisle Baker, 25 Glenland Rd., Chestnut Hill, Mass. 02167 [22] Filed: Oct. 24, 1972 [21] Appl. No.: 299,678

[52] US. Cl 52/81, 52/82, 52/DIG. 1O [51] Int. Cl E04b l/34, EO4b 7/08 [58] Field of Search 52/80, 81, 83, DIG. 10, 52/237 [56] References Cited UNITED STATES PATENTS 2,839,841 6/1958 Berry 52/DIG. 10 2,918,992 12/1959 Gelsavage.... 52/81 3,093,461 6/1963 Woolven 52/DIG. 10

3,153,235 10/1964 Chatelain 52/2 3,584,400 6/1973 Voges 52/DIG. 10 3,659,360 5/1972 'Zeischegg 52/D1G. 10

OTHER PUBLICATIONS Philosophical Transactions of the Royal Society A 246 Mathematical Models by Cundy & Rollett; Oxford U. Press 1961, PP- 82, 83, 90, 91, 96, 97 9 99, 110 .11.1 1,34, 135, 144-155.

Primary ExaminerFrank L. Abbott Assistant ExaminerHenry Raduazo Attorney, Agent, or FirmRichard J. Birch [5 7 ABSTRACT A space enclosing structure formed from a plurality of trapezoidal structural elements. The trapezoidal elements are assembled in groups of five each to form a plurality of pentagonal based, truncated pyramidal modules. The modules in turn are assembled in abutting base edge'to-base edge relationship to form at least a portion of a spheroid.

9 Claims, 8 Drawing Figures PATENTEL BEE! 71974 sum 10F 2 PATENm EEC] 7 I914 SHEET 20F 2 Lil is I 1 SPACE ENCLOSING STRUCTURE BACKGROUND OF THE INVENTION The present invention relates to space enclosing structures in general and, more particularly, a space enclosing structure which utilizes one basic shape to define the enclosed space.

Dome shaped structures, such as geodesic domes, are well known to the art. Most dome shaped structures are based on a variation of the triangle using a composite of linear elements which often require at least six sprocket joints at each major intersection. Of less theoretical purity, but perhaps of greater practicability is a structural design composed of surfaces rather than linear elements overlaid with a skin. One such panel type structure is described by R. Buckminster Fuller in the May, 1972 issue of Popular Scienceat Pages 128-l3 l. The patent literature also describes various types of panel or sheet domed structures in U.S. Pat. No. 3,34l,989 issued Sept. 19, 1967. See also Geodesic Geometry by Jonathon Kanter, published in Domebook 2 by Kahn, et al., May, 1971 and the bibliography therein.

It is a general object of the present invention to provide a space enclosing structure using a single basic geometrically shaped structural element.

It is a specific object of the present invention to provide a space enclosing structure which is based upon the repetitive use of a trapezoidal structural element which has equal base angles.

It is another object of the invention to provide a space enclosing structure which can be constructed from a minimum number of identically shaped structural elements.

It is a feature of the invention that the individual structure elements can be assembled with relatively simple mechanical interconnections and do not require complicated multi-element fasteners at the major intersections.

It is another feature of the invention that the appearance of the structure can be varied by altering the face angles of the trapezoidal structural element.

It is still another feature of the invention that the resulting shape is aesthetically pleasing and can be used for a variety of purposes.

These objects and other objects and features of the invention will best be understood from a detailed description of a preferred embodiment thereof, selected for purposes of illustration and shown in the accompanying drawings in which:

FIG. la is a diagram of the basic trapezoidal structural element employed in constructing the space enclosing structure of the invention;

FIG. lb is a perspective view of a space enclosing structure using the structural element of FIG. 1a;

FIG. 2 is a perspective view of a portion of the space enclosing structure which illustrates the effect of varying the face angles of the trapezoidal structural element;

FIG. 3 is a perspective view of a portion of the space enclosing structure showing another variation in form which is achieved by altering the face angles of the trapezoidal structural element;

FIG. 4 is a diagrammatic view of a portion of the space enclosing structure showing a four color configuration for the structure;

FIG. 5 is a perspective view of another embodiment of the invention;

FIG. 6 is a view in cross-section showing the hinged connection of two trapezoidal structural elements; and,

trapezoidal structural elements 12. The trapezoidal structural element is shown in detail in FIG. 1a. The element 12 has a trapezoidal shape with equal angle base angles a and b. The four sides of the trapezoidal structural element 12 are identified as follows: trapezoid base 12a, non-parallel side 12b, parallel side 1213 and non-parallel side 12d. Although the two non-parallel sides 12b and 12d are shown in FIG. 10 as being of equal length to form an isosceles trapezium, it should be understood that the invention is not so limited and that the non-parallel sides 12b and 12d of the trapezoidal element 12 can be of unequal length. If the nonparallel sides 12b and 12d are extended as shown by the dashed lines in FIG 1a, they define a vertex angle e. The numerical relationship of the base angles a and b and the vertex angle e will be discussed below.

Referring now to FIG. 1b, the trapezoidal structural elements 12 are assembled in groups of five each to form pentagonal based, truncated pyramidal modules indicated generally by the reference numeral 13. The modules 13 are in turn assembled in abutting base edge-to-base edge relationship to form at least a portion of a spheroid. A complete spheroid is formed by the assembly of twelve modules 13 as shown in FIG. lb. For a dome shaped structure, a partial spheroid is formed from less than twelve modules.

In the preferred embodiment, the upper edges 12c of the five trapezoidal elements lie within a single truncation plane and define a pentagonal area 14. The pentagonal area 14 can be left open or enclosed by a corresponding pentagonal shaped element.

The abutting trapezoidal elements 12 of two truncated pyramidal modules 13 define a hexagonal area 16 as shown in FIG. 1b. The base line between the two abutting trapezoidal bases 12a is located further from the center of the spheroid than the corresponding trapezoidal parallel edges 120. In other words, the hexagonal area 16 can be viewed as being convex outwardly from the center of the spheroid. This particular configuration is achieved by using equal trapezoidal base angles a and b which are greater than 54 and less than 58. The corresponding range for the vertex angle e is greater than 64 and less than 72.

It already has been mentioned that the configuration of the space enclosing structure 10 can be altered by varying the face angles of the trapezoidal structural elements 12. Thus, for example, referring to FIG. 2, the hexagonal area 16 is negative or concave inwardly toward the center of the spheroid. This configuration is attained by using equal base angles a and b which are in the range of greater than 58 and less than The corresponding range for the vertex angle e is greater than 0 and less than 64.

FIG. 3 illustrates still another configuration of the spheroid in which the hexagonal areas 16 are substantially planar. Based upon my experiments, I have found that a base angle of approximately 58 for the base angles a and b and a corresponding vertex angle of 64 produces a substantially fiat hexagonal area 16.

Although the preceding description has been directed to an isosceles trapezoidal element as shown in FIG. 1a, it should be understood that the invention is not so limited and that the non-parallel sides 12b and 12d of the trapezoidal structural element 12 can be of unequal length. Given this condition, it will be appreciated that the resulting pyramidal modules 13 will be truncated by a oblique plane of truncation. Other variations in the configuration of the space enclosing structure can be achieved by changing the directional relationship of the trapezoidal base 12a and the parallel side 12c. For example, comparing FIGS. 1b and 5, it can be seen that in FIG. lb the parallel sides 12c are located further mt s arts! q lhs hsr islthaathe trapezoidal bases 12a. The converse situation is depicted in FIG. in which the truncated pyramidal modules extend inwardly toward the center of the spheroid. In this situation, the trapezoidal bases 12a are located further from the center of the spheroid than their corresponding parallel sides 120.

The space enclosing structure of the present invention can be employed for a wide variety of purposes. For example, the enclosure can be used as a building for residential or commercial occupancy. At the other end of the spectrum, the structure can be used as a lamp shade with the trapezoidal elements comprising stained glass panels. In the latter configuration, and other uses involving a color pattern, the space enclosing structure of the present invention can be employed to solve the so-called four color problem.

Referring to FIG. 4, the four colors are indicated by the capital letters A, B, C and W. It can be seen from an inspection of FIG. 4 that the hexagonal areas 16 are colored A, B, and C while the pentagonal portion 14 is colored W. Given this arrangement, it will be appreciated that no hexagonal portion of one color abuts another hexagonal portion of the same color, thereby, providing a solution for the four color problem.

One of the advantages of the present invention is that the trapezoidal structural elements 12 can be easily assembled and interconnected without requiring complex fastening members. For example, referring to FIG. 6, there is shown in crosssection portions of two trapezoidal structural elements 12 which are secured together by means of a hinge assembly indicated generally by the reference numeral 18. The trapezoidal panels are held within C-shaped portions 18a and 18b of the hinge assembly. Of course, other fastening systems can be employed to join the abutting edges of the various trapezoidal elements 12. In the case of the previously mentioned stained glass lamp shade, standard stained glass techniques, e.g., lead caning or copper foil and solder, are employed to join the structural elements.

The space enclosing structure illustrated in FIGS. 1 through 3 and 5 depict a spheroid with seventy-two elements. If a larger spheroid is desired, additional pentagonal modules can be assembled on top of the basic pentagonal modules shown in the Figures and identified by the reference numeral 13. For example, looking at FIG. 7, there are shown two superposed trapezoidal modules which are formed from two groups of trapezoidal structural elements 12 and 12. The individual trapezoidal elements 12 have different face angles from the trapezoidal elements 12. It will be appreciated that additional trapezoidal elements can be assembled on top of the elements indicated by the reference numeral 12'.

Various materials can be used to form the trapezoidal structural elements of the present invention. For instance, the element can be made of wood, steel, plastic, glass and the like. Similarly, the elements themselves can be planar or curved, provided that the edges 12a through 12d lie in a common plane.

Havingsdescribed in detail the preferred embodiment of my invention, it will now be apparent to those skilled in the art that numerous modifications can be made therein without departing from the scope of the invention as defined in the following claims.

What I claim and desire to secure by Letters Patent of the United States is:

l. A space enclosing structure comprising:

a plurality of trapezoidal structural elements having equal base angles not greater than 58 or less than 54 and assembled in groups of five each to form a plurality of outwardly extending, pentagonal based, truncated pyramidal modules, said modules being assembled in abutting base edge-to-base edge relationship to form at least a portion of a spheroid.

2. The structure of claim 1 wherein 12 of said pyramidal modules are assembled to form a complete spheroid.

3. The structure of claim 1 further comprising at least one pentagonal structural element positioned within the truncated portion of one of said pyramidal modules and secured with respect to the shorter parallel portion of each one of the five trapezoidal structural elements which form said pyramidal module with the longer parallel portion of each trapezoidal structural element abutting the longer parallel portion of another trapezoidal structural element.

4. The structure of claim 1 wherein said trapezoidal structural elements have equal length non-parallel sides. I

5. The structure of claim 1 wherein the truncation plane intersects the truncated pyramidal module to form a pentagonal area.

6. The structure of claim 1 wherein the four sides of said trapezoidal structural element are of unequal lengths.

7. The apparatus of claim 2 wherein the abutting base edge-to-base edge trapezoidal structural elements of the pyramidal modules define hexagonal portions of the structure and wherein the truncation plane intersects the truncated pyramidal module to form a pentagonal area, a pentagonal structural element positioned within said pentagonal area and fixed with respect to the trapezoidal structural elements, said pentagonal elements having a first color and the hexagonal portions surrounding said pentagonal elements having three other colors with said four colors all being different from each other and with no hexagonal portion of one color abutting another hexagonal portion of the same color.

8. The structure of claim 1 wherein the abutting base edge-to-base edge trapezoidal structural elements of two pyramidal modules define'a hexagonal portion of the structure with said hexagonal portion being convex outwardly from the center of the spheroid.

9. A space enclosing structure comprising:

6 with the abutting base edge-to-base edge trapezoidal structural elements of two of said pyramidal modules defining a planar hexagonal portion of the structure. 

1. A space enclosing structure comprising: a plurality of trapezoidal structural elements having equal base angles not greater than 58* or less than 54* and assembled in groups of five each to form a plurality of outwardly extending, pentagonal based, truncated pyramidal modules, said modules being assembled in abutting base edge-to-base edge relationship to form at least a portion of a spheroid.
 2. The structure of claim 1 wherein 12 of said pyramidal modules are assembled to form a complete spheroid.
 3. The structure of claim 1 further comprising at least one pentagonal structural element positioned within the truncated portion of one of said pyramidal modules and secured with respect to the shorter parallel portion of each one of the five trapezoidal structural elements which form said pyramidal module with the longer parallel portion of each trapezoidal structural element abutting the longer parallel portion of another trapezoidal structural element.
 4. The structure of claim 1 wherein said trapezoidal structural elements have equal length non-parallel sides.
 5. The structure of claim 1 wherein the truncation plane intersects the truncated pyramidal module to form a pentagonal area.
 6. The structure of claim 1 wherein the four sides of said trapezoidal structural element are of unequal lengths.
 7. The apparatus of claim 2 wherein the abutting base edge-to-base edge trapezoidal structural elements of the pyramidal modules define hexagonal portions of the structure and wherein the truncation plane intersects the truncated pyramidal module to form a pentagonal area, a pentagonal structural element positioned within said pentagonal area and fixed with respect to the trapezoidal structural elements, said pentagonal elements having a first color and the hexagonal portions surrounding said pentagonal elements having three other colors with said four colors all being different from each other and with no hexagonal portion of one color abutting another hexagonal portion of the same color.
 8. The structure of claim 1 wherein the abutting base edge-to-base edge trapezoidal structural elements of two pyramidal modules define a hexagonal portion of the structure with said hexagonal portion being convex outwardly from the center of the spheroid.
 9. A space enclosing structure comprising: a plurality of trapezoidal structural elements having equal base angles and assembled in groups of five each to form a plurality of pentagonal based, truncated pyramidal modules, said modules being assembled in abutting base edge-to-base edge relationship to form at least a portion of a spheroid with the abutting base edge-to-base edge trapezoidal structural elements of two of said pyramidal modules defining a planar hexagonal portion of the structure. 